\subsection{Quality Measures}
\noindent The quality measure of a grasp should take into account if the body to be grasped is in form or force closure. Furthermore a good grasp can be identified as a grasp that can resist as large disturbance forces as possible on the object. If a robot is to grasp an object, one should consider how well the robot can move after grasping the object, as well as making the robot efficient by moving the smallest possible distance. In this project the focus will however be on the gripper and object. It is assumed that the objects to grasp are rigid, and does not break if large forces are applied. In reality some objects are fragile and the forces applied by a hand should be at a minimum.\\

\noindent In the following subsections the principle and theory behind two different quality measures will be presented, respectively CMCCP and Wrench Space.
\input{pages/ccmp.tex}

\input{pages/force.tex}

\noindent The wrench space measure has some drawbacks when one need to be able to compare the quality measure with a real physical entity like the force. There is an additive force problem which means that if one force, $F$, is applied at a specific contact point, this will not result in the same convex hull as if two forces of size $\frac{F}{2}$ is to be applied at a infinitely small distance apart at the same contact point.\\
A similar problem exists when considering the torques. If a two-finger gripper is used, the gripper will be able to resist a torque in each finger. In reality the torque that the hand is able to resist is then the two torques added with each other. The convex hull will however see this as two smaller torques instead of one large torque.\\

\noindent A task specific solution to these problems can be found. For the additive force problem, we use the fact that a two finger gripper is going to be used. One approach would be to simply merge all the found contact points into only two large contact points. This will however decrease the stability of the convex hull algorithm, because of problems with the high-dimensional geometry. Therefore another approach has been used. All normal forces are scaled. The sum of the size of all normal forces is found, and all normal forces is then scaled according to the following:
\begin{equation}
\lambda _F = \frac{\frac{1}{2}\sum F_n}{min(F_n)}
\label{eq:lambda:force}
\end{equation}\\
The factor, $\frac{1}{2}$, is used because it is assumed that half of the total force is on one finger, and the other half on the other finger.\\

\noindent As a solution to the torque problem, the following scaling is performed of the torque:
\begin{equation}
\lambda _\tau = \frac{2}{\mbox{MaxDistance}}
\label{eq:lambda:torque}
\end{equation}
The factor, 2, is used as it is known that a two-finger gripper is used. Therefore the torque that the hand is actually able to resist can be expected to be twice as big.